Impulse wave diffraction on a permittivity step in a waveguide

The paper deals with the impulse solution of the Klein-Gordon equation that describes, in the time domain (TD), the propagation of waves in a waveguide, plane waves in a plasma, and wave beams in free space. We consider the basic problem of impulse diffraction on a permittivity step in a waveguide. A generalized scattering matrix in TD approach is used to express the solution in a closed-form. Transmission and reflection operators are obtained. To illustrate the solution, some energy flow diagrams, which show the space-time distribution of energy density and energy flow speed, are used.